Councils deemed to have let down children in their care face having their responsibilities handed over to another local authority or sub-contracted out to the private sector or charities under new plans to be announced on Monday by David Cameron.

The government will separately publish data on how local authorities perform on adoption as part of a move to allow people to challenge councils they believe are failing through inefficiency or poor performance.

The prime minister told the Times a green paper would set out new minimum standards for the proportion of children who should be adopted from care each year and impose time limits on the process.

"I see [the new policy] as a range of 'floor standards' including the educational attainment of children in care, placement stability, proportion of children adopted from care and the timeliness of adoption," he said.

Responding to figures showing a sharp decline in the number of babies who find permanent new families, Cameron will say today that it is unacceptable that some councils have been allowed to let down children for so long as he launches a national campaign on adoption and fostering.

"It is shocking that, of the 3,600 children under the age of one in care, only 60 were adopted last year – this is clearly not good enough," the prime minister will say at the launch of the Give a Child a Home campaign, which calls on more members of the public to come forward as adopters and foster parents. "We will publish data on how every local authority is performing to ensure they are working quickly enough to provide the safe and secure family environment every child deserves."

New data on the Department of Education's website will enable people to see how their local authority is doing on issues such as adoption rates and the educational attainment of children in care in comparison with others.

Where councils are deemed to be failing, adoption services could either be privatised and handed to independent agencies or taken over by higher performing local authorities.

Its author, David Norgrove, has already called for court cases, which can cause delays to adoption, to be restricted to six months, rather than the current average of 13 months.

Councils have blamed lengthy courtroom battles, a decline in potential adoptive parents and complex family problems for holdups. The average wait for adoption is now two years and seven months.

Cameron, who is meeting parents, carers and adoption services representatives, will launch the website www.giveachildahome.co.uk, which aims to open debate on reform and provide information on adopting and fostering.

He will say: "We need more people to think about fostering and adoption so, this National Adoption Week, I would encourage anyone who is considering adoption to find out more about whether they could provide a home for a child."